A tire-air-pressure-generating apparatus of such a type is disclosed in, for example, Japanese Patent Application Laid-Open (kokai) No. 1-172003. In the tire-air-pressure-generating apparatus described in this publication, a pump unit is disposed in a hub section of a wheel (composed of a wheel body and a tire); i.e., a hub section (a central portion) of the wheel body), and carries out a reciprocating motion in the axial direction of an axle while one end of a piston of the pump unit is in contact with an inclined surface of a cam member, which is stationary in relation to the rotating wheel. Therefore, as the wheel rotates, the piston of the pump unit reciprocates, thereby yielding a pumping function.